As sad as it is to say I believe the only way to get rid of them is a chemical treatment. Snails that are pesky ones like this can find all sorts of food so attempting to starve them off will barley dent the population. I also doubt any snail predators will get rid of all of them from what it sounds and it will only reduce a fraction of what will be reproducing.
I once had a snail problem that could not be stopped and adding more and more animals to feed on them didn't help reduce the population of snails but did put more stress on my bio filtration so in the end I took out what ever I had such as bio wheels, sponges,...etc,..etc, anything that helped harbor my bio filtration and added it all to another aged aquarium. Then after all that I zapped them with some snail treatment.
I did some big water changes using my DI machine and added some carbon back to my aquarium and after a week or two I put all the stuff I took out such as sponges and bio wheels,..etc,...etc back in. Still did some slight damage and things were slightly unstable for a few days ( maybe 2 ) but it got them all.